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Nesting Cubes, Recursive Cubes, Cubes within Cubes

p2.PNG Nesting Cubes, Recursive Cubes, Cubes within Cubes
p1.PNG Nesting Cubes, Recursive Cubes, Cubes within Cubes
p3.PNG Nesting Cubes, Recursive Cubes, Cubes within Cubes
sevenBot.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
sevenTop.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
fiveTop.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
fiveBot.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
threeBot.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
threeTop.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
unitcube.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
sevenBot_Loose.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
fiveBot_Loose.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
threeBot_Loose.stl Nesting Cubes, Recursive Cubes, Cubes within Cubes
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Creation quality: 5.0/5 (1 vote)
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  • 2.3k views
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  • 46 downloads
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3D design format
STL Folder details Close
  • fiveBot.stl
  • fiveBot_Loose.stl
  • fiveTop.stl
  • sevenBot.stl
  • sevenBot_Loose.stl
  • sevenTop.stl
  • threeBot.stl
  • threeBot_Loose.stl
  • threeTop.stl
  • unitcube.stl

Learn more about the formats
Publication date 2019-12-02 at 15:38
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Published to Thingiverse on: 2019-12-01 at 20:51
Design number 88998
LGBU

LGBU

3D printer file info

3D model description

####Nesting Cubes, Recursive Cubes, Cubes within Cubes

This design is a 7-cube that has a 5-cube that has a 3-cube that has a unit cube. Each unit cube is 10 mm^3. Tolerance is added to allow the cubes to slide (nest) into each other.

####About the files
1. Each cube has a bottom part and a top cover.
2. The regular versions have a 0.4 mm clearance all around; the loose versions have a 0.5mm clearance.
3. The top covers are the same as the clearance is added to the shells. The 3-cube top is the same as the unit cube.

In addition to the recursive and geometric structures, there are a few questions to explore:

  1. How does the volume of a cube increase as we change the cube edge length from 1 unit, to 3, 5, and 7 units?
  2. What is the difference between the volume of the 7-cube and that of the 5-cube?
  3. How does one count the number of unit cubes if we take a 5-cube core out of a 7-cube? If one counts 7^2 cube on each face and multiply that by six, how should the number be adjusted to find the actual number of unit cubes? Hints: Each vertex is counted three times; each edge is counted two times.
  4. Pose your own questions.

####References
1. Cubic numbers. http://mathworld.wolfram.com/CubicNumber.html
2. https://en.wikipedia.org/wiki/Recursion
3. https://en.wikipedia.org/wiki/Matryoshka_doll

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